For work purposes I was looking around trying to understand which constraint we have from observations to the equation of state of the dark matter. It turns out that we don't know that much. If from CMB, SNIa nad LSS we can constraint w=0 with high precision, not the same accuracy on small scales.

What do you mean by equation of state? On largest scales dark matter and baryons are dust with w=0. On small scales baryons are no longer dust (e.g. could be ideal gas with p dependent not only on ρ) but for DM I think we would first need to understand what it is made of to speak of some specific equation of state. Still, as it doesn't interact electromagnetically, I can hardly imagine associating some pressure to it? Perhaps I'm wrong.

I'm pretty sure the basic answer is that if you believe WMAP andH0 measurements, then you really can't have very much dark matter that's warm, for much the same reasons you get limits on the total mass in neutrinos. WDM streaming out of potential wells would mess up the power spectrum on small scales in a rather noticable way (especially now with ACT and SPT, I'm not sure the H0 prior is still even necessary).

In addition to the WDM question (and related constraints coming from neutrino masses), unusual equations of state (and, correspondingly, unusual sound speeds) are a long-running topic – http://background.uchicago.edu/~whu/Papers/gdm.pdf is a classic reference. DM cross-sections (related to w and cs questions) became a question empirically with the discovery of the bullet cluster (and related objects.) I would be surprised if CAMB these days did not allow you to try a range of w(z) and cs(z) curves.